I had a bunch of files being moved to a directory when it's cancelled on accident. How Can I resume it rather than overwriting all of them ? How does Linux tell, if any, whether a files need to be overwrite or resume?

For instance, A.mp3 is 30MB and only 10MB of them has moved to the target directory. Now they both have the same name. Does Linux know whether to resume it?

If it's not possible to resume it with the mv command or midnight commander, How such thing is possible with other softwares? Using a mirroring utility next time instead of the mv command?

BTW, Is there a way to show progress while moving files? mv -v doesn't help.

I don't understand the first part of your question. Are both files now 30MB? 10MB? or somewhere in between?

If you use Konqueror, it shows your progress while moving files.
cheers,
jdk

Try `mv -u`. You can manually delete the source files after that. Copy the one file that's half done manually or `touch A.mp3` first (that being the original) to make sure mv moves it. Linux applications generally make this decision based on mtime or ctime, which is when the file's contents or attributes were last modified, respectively.

Vis. "midnight commander" it will ask if you want to replace files with duplicate names when doing a batch move.